The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  1  0  1  1  1  2  8  1  1  2  1  2  1  0 12  2  1  8  1  2  1 12  1  0  8  8  2  8  4  0  1  1  1
 0  2  0  6  0  6  0  2  4  6 10 12  4 14 10  0  2  4 14  8 14  2 14  2  2  8 10  8  6  2  6  6  6  8 10  0  2  2 10 14  2  0  8  4  2  0  4  8  8 14  8  2  4  6 14  8
 0  0 12  0  0  0  4  0 12  0  8 12  0  4 12  8 12  4  8  8  4  4  8 12  0 12  8 12  0  0  4  4  0  8  4 12 12  8  0  8  4 12  8  8  0  8  0  8  8  4  4  8  4  8  4  0
 0  0  0 12  0  0  0  4  8  4  4  0  0 12 12 12  8 12  0 12  8  0  8  8  0 12 12  4  4  8  8 12  8  8  4  4  4 12 12  4  4 12  4  4 12  0 12  4  8  8 12  8  0 12  4  4
 0  0  0  0 12  0  4  8  0  4 12  4  4 12  8 12  8  0 12  0  8  0  4  8  8  8  4  4 12  4  4  4  8  0  0 12  0 12 12  0 12  4  0  0 12  4 12  4  4  8  4 12 12  8 12  0
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  0  0  8  0  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0  8  0  0  0  0  8

generates a code of length 56 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+46x^46+106x^47+231x^48+446x^49+768x^50+1080x^51+1770x^52+2542x^53+3223x^54+4002x^55+4256x^56+4220x^57+3349x^58+2386x^59+1747x^60+1042x^61+725x^62+360x^63+161x^64+124x^65+71x^66+62x^67+23x^68+8x^69+10x^70+4x^71+3x^72+2x^73

The gray image is a code over GF(2) with n=448, k=15 and d=184.
This code was found by Heurico 1.16 in 18.2 seconds.